This paper investigates the prescribed performance control problem for a vehicular platoon (i.e., a group of vehicles that travels in close proximity to one another, nose-to-tail, at highway speeds) simultaneously considering actuator faults and saturation. In the first case, a Gaussian error function (GEF) is applied to replace the nonsmooth actuator saturation of each vehicle in a smooth way. Then, a finite-time prescribed performance function (FNPPF) is proposed, which guarantees the tracking error of the platoon system converges to a predetermined region in a defined time. Subsequently, by combing the fuzzy-logic system (FLS) and parameter learning algorithm, an adaptive control scheme is developed in the context of sliding mode control, which guarantees all signals in the closed-loop system are practically finite-time stable. Finally, numerical simulations are carried out for a six-vehicle platoon to show the effectiveness of the proposed algorithm.